I can understand why you would have that reasoning, but SSRIs are commonly prescribed off label to populations for non-mental health related reasons, for example ED or urinary incontinence, and in these populations the relationship holds, leading to some governments and regulatory bodies to recommend or warn against use for these conditions.
"Although duloxetine reduced the symptoms of stress urinary incontinence and improved women’s quality of life, the harms related to suicidality and violence were 4 to 5 times more common with duloxetine than with a placebo, a meta analysis using patient level data by researchers from the Nordic Cochrane Centre showed."
https://www.bmj.com/content/355/bmj.i6103
"Although duloxetine reduced the symptoms of stress urinary incontinence and improved women’s quality of life, the harms related to suicidality and violence were 4 to 5 times more common with duloxetine than with a placebo, a meta analysis using patient level data by researchers from the Nordic Cochrane Centre showed." https://www.bmj.com/content/355/bmj.i6103